The proofs in this work mirror those in [1]}, but apart from adding the assumption of strand symmetry and removing the assumption of an unrooted tree, we also relax an important assumption that [1]} makes about the structure of the model. As noted in [3]} and addressed in [4]} the model of [5]} is only identifiable up to an arbitrary relabelling of states at internal nodes of the phylogeny. [1]} addresses this problem by assuming that the transition probability matrix for every edge in the topology is reconstructible from rows. As we shall demonstrate, this assumption can be restrictive in practice, so, motivated by Remark 4 in [1]}, we partially relax it.
